ager@chromium.org | 01fe7df | 2010-11-10 11:59:11 +0000 | [diff] [blame] | 1 | // Copyright 2010 the V8 project authors. All rights reserved. |
| 2 | // Redistribution and use in source and binary forms, with or without |
| 3 | // modification, are permitted provided that the following conditions are |
| 4 | // met: |
| 5 | // |
| 6 | // * Redistributions of source code must retain the above copyright |
| 7 | // notice, this list of conditions and the following disclaimer. |
| 8 | // * Redistributions in binary form must reproduce the above |
| 9 | // copyright notice, this list of conditions and the following |
| 10 | // disclaimer in the documentation and/or other materials provided |
| 11 | // with the distribution. |
| 12 | // * Neither the name of Google Inc. nor the names of its |
| 13 | // contributors may be used to endorse or promote products derived |
| 14 | // from this software without specific prior written permission. |
| 15 | // |
| 16 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 17 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| 18 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 19 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| 20 | // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 21 | // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| 22 | // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| 23 | // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| 24 | // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 25 | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 26 | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 27 | |
| 28 | #include "v8.h" |
| 29 | |
| 30 | #include "bignum.h" |
| 31 | #include "utils.h" |
| 32 | |
| 33 | namespace v8 { |
| 34 | namespace internal { |
| 35 | |
| 36 | Bignum::Bignum() |
| 37 | : bigits_(bigits_buffer_, kBigitCapacity), used_digits_(0), exponent_(0) { |
| 38 | for (int i = 0; i < kBigitCapacity; ++i) { |
| 39 | bigits_[i] = 0; |
| 40 | } |
| 41 | } |
| 42 | |
| 43 | |
| 44 | template<typename S> |
| 45 | static int BitSize(S value) { |
| 46 | return 8 * sizeof(value); |
| 47 | } |
| 48 | |
| 49 | // Guaranteed to lie in one Bigit. |
| 50 | void Bignum::AssignUInt16(uint16_t value) { |
| 51 | ASSERT(kBigitSize >= BitSize(value)); |
| 52 | Zero(); |
| 53 | if (value == 0) return; |
| 54 | |
| 55 | EnsureCapacity(1); |
| 56 | bigits_[0] = value; |
| 57 | used_digits_ = 1; |
| 58 | } |
| 59 | |
| 60 | |
| 61 | void Bignum::AssignUInt64(uint64_t value) { |
| 62 | const int kUInt64Size = 64; |
| 63 | |
| 64 | Zero(); |
| 65 | if (value == 0) return; |
| 66 | |
| 67 | int needed_bigits = kUInt64Size / kBigitSize + 1; |
| 68 | EnsureCapacity(needed_bigits); |
| 69 | for (int i = 0; i < needed_bigits; ++i) { |
| 70 | bigits_[i] = value & kBigitMask; |
| 71 | value = value >> kBigitSize; |
| 72 | } |
| 73 | used_digits_ = needed_bigits; |
| 74 | Clamp(); |
| 75 | } |
| 76 | |
| 77 | |
| 78 | void Bignum::AssignBignum(const Bignum& other) { |
| 79 | exponent_ = other.exponent_; |
| 80 | for (int i = 0; i < other.used_digits_; ++i) { |
| 81 | bigits_[i] = other.bigits_[i]; |
| 82 | } |
| 83 | // Clear the excess digits (if there were any). |
| 84 | for (int i = other.used_digits_; i < used_digits_; ++i) { |
| 85 | bigits_[i] = 0; |
| 86 | } |
| 87 | used_digits_ = other.used_digits_; |
| 88 | } |
| 89 | |
| 90 | |
| 91 | static uint64_t ReadUInt64(Vector<const char> buffer, |
| 92 | int from, |
| 93 | int digits_to_read) { |
| 94 | uint64_t result = 0; |
| 95 | for (int i = from; i < from + digits_to_read; ++i) { |
| 96 | int digit = buffer[i] - '0'; |
| 97 | ASSERT(0 <= digit && digit <= 9); |
| 98 | result = result * 10 + digit; |
| 99 | } |
| 100 | return result; |
| 101 | } |
| 102 | |
| 103 | |
| 104 | void Bignum::AssignDecimalString(Vector<const char> value) { |
| 105 | // 2^64 = 18446744073709551616 > 10^19 |
| 106 | const int kMaxUint64DecimalDigits = 19; |
| 107 | Zero(); |
| 108 | int length = value.length(); |
| 109 | int pos = 0; |
| 110 | // Let's just say that each digit needs 4 bits. |
| 111 | while (length >= kMaxUint64DecimalDigits) { |
| 112 | uint64_t digits = ReadUInt64(value, pos, kMaxUint64DecimalDigits); |
| 113 | pos += kMaxUint64DecimalDigits; |
| 114 | length -= kMaxUint64DecimalDigits; |
| 115 | MultiplyByPowerOfTen(kMaxUint64DecimalDigits); |
| 116 | AddUInt64(digits); |
| 117 | } |
| 118 | uint64_t digits = ReadUInt64(value, pos, length); |
| 119 | MultiplyByPowerOfTen(length); |
| 120 | AddUInt64(digits); |
| 121 | Clamp(); |
| 122 | } |
| 123 | |
| 124 | |
| 125 | static int HexCharValue(char c) { |
| 126 | if ('0' <= c && c <= '9') return c - '0'; |
| 127 | if ('a' <= c && c <= 'f') return 10 + c - 'a'; |
| 128 | if ('A' <= c && c <= 'F') return 10 + c - 'A'; |
| 129 | UNREACHABLE(); |
| 130 | return 0; // To make compiler happy. |
| 131 | } |
| 132 | |
| 133 | |
| 134 | void Bignum::AssignHexString(Vector<const char> value) { |
| 135 | Zero(); |
| 136 | int length = value.length(); |
| 137 | |
| 138 | int needed_bigits = length * 4 / kBigitSize + 1; |
| 139 | EnsureCapacity(needed_bigits); |
| 140 | int string_index = length - 1; |
| 141 | for (int i = 0; i < needed_bigits - 1; ++i) { |
| 142 | // These bigits are guaranteed to be "full". |
| 143 | Chunk current_bigit = 0; |
| 144 | for (int j = 0; j < kBigitSize / 4; j++) { |
| 145 | current_bigit += HexCharValue(value[string_index--]) << (j * 4); |
| 146 | } |
| 147 | bigits_[i] = current_bigit; |
| 148 | } |
| 149 | used_digits_ = needed_bigits - 1; |
| 150 | |
| 151 | Chunk most_significant_bigit = 0; // Could be = 0; |
| 152 | for (int j = 0; j <= string_index; ++j) { |
| 153 | most_significant_bigit <<= 4; |
| 154 | most_significant_bigit += HexCharValue(value[j]); |
| 155 | } |
| 156 | if (most_significant_bigit != 0) { |
| 157 | bigits_[used_digits_] = most_significant_bigit; |
| 158 | used_digits_++; |
| 159 | } |
| 160 | Clamp(); |
| 161 | } |
| 162 | |
| 163 | |
| 164 | void Bignum::AddUInt64(uint64_t operand) { |
| 165 | if (operand == 0) return; |
| 166 | Bignum other; |
| 167 | other.AssignUInt64(operand); |
| 168 | AddBignum(other); |
| 169 | } |
| 170 | |
| 171 | |
| 172 | void Bignum::AddBignum(const Bignum& other) { |
| 173 | ASSERT(IsClamped()); |
| 174 | ASSERT(other.IsClamped()); |
| 175 | |
| 176 | // If this has a greater exponent than other append zero-bigits to this. |
| 177 | // After this call exponent_ <= other.exponent_. |
| 178 | Align(other); |
| 179 | |
| 180 | // There are two possibilities: |
| 181 | // aaaaaaaaaaa 0000 (where the 0s represent a's exponent) |
| 182 | // bbbbb 00000000 |
| 183 | // ---------------- |
| 184 | // ccccccccccc 0000 |
| 185 | // or |
| 186 | // aaaaaaaaaa 0000 |
| 187 | // bbbbbbbbb 0000000 |
| 188 | // ----------------- |
| 189 | // cccccccccccc 0000 |
| 190 | // In both cases we might need a carry bigit. |
| 191 | |
| 192 | EnsureCapacity(1 + Max(BigitLength(), other.BigitLength()) - exponent_); |
| 193 | Chunk carry = 0; |
| 194 | int bigit_pos = other.exponent_ - exponent_; |
| 195 | ASSERT(bigit_pos >= 0); |
| 196 | for (int i = 0; i < other.used_digits_; ++i) { |
| 197 | Chunk sum = bigits_[bigit_pos] + other.bigits_[i] + carry; |
| 198 | bigits_[bigit_pos] = sum & kBigitMask; |
| 199 | carry = sum >> kBigitSize; |
| 200 | bigit_pos++; |
| 201 | } |
| 202 | |
| 203 | while (carry != 0) { |
| 204 | Chunk sum = bigits_[bigit_pos] + carry; |
| 205 | bigits_[bigit_pos] = sum & kBigitMask; |
| 206 | carry = sum >> kBigitSize; |
| 207 | bigit_pos++; |
| 208 | } |
| 209 | used_digits_ = Max(bigit_pos, used_digits_); |
| 210 | ASSERT(IsClamped()); |
| 211 | } |
| 212 | |
| 213 | |
| 214 | void Bignum::SubtractBignum(const Bignum& other) { |
| 215 | ASSERT(IsClamped()); |
| 216 | ASSERT(other.IsClamped()); |
| 217 | // We require this to be bigger than other. |
| 218 | ASSERT(LessEqual(other, *this)); |
| 219 | |
| 220 | Align(other); |
| 221 | |
| 222 | int offset = other.exponent_ - exponent_; |
| 223 | Chunk borrow = 0; |
| 224 | int i; |
| 225 | for (i = 0; i < other.used_digits_; ++i) { |
| 226 | ASSERT((borrow == 0) || (borrow == 1)); |
| 227 | Chunk difference = bigits_[i + offset] - other.bigits_[i] - borrow; |
| 228 | bigits_[i + offset] = difference & kBigitMask; |
| 229 | borrow = difference >> (kChunkSize - 1); |
| 230 | } |
| 231 | while (borrow != 0) { |
| 232 | Chunk difference = bigits_[i + offset] - borrow; |
| 233 | bigits_[i + offset] = difference & kBigitMask; |
| 234 | borrow = difference >> (kChunkSize - 1); |
| 235 | ++i; |
| 236 | } |
| 237 | Clamp(); |
| 238 | } |
| 239 | |
| 240 | |
| 241 | void Bignum::ShiftLeft(int shift_amount) { |
| 242 | if (used_digits_ == 0) return; |
| 243 | exponent_ += shift_amount / kBigitSize; |
| 244 | int local_shift = shift_amount % kBigitSize; |
| 245 | EnsureCapacity(used_digits_ + 1); |
| 246 | BigitsShiftLeft(local_shift); |
| 247 | } |
| 248 | |
| 249 | |
| 250 | void Bignum::MultiplyByUInt32(uint32_t factor) { |
| 251 | if (factor == 1) return; |
| 252 | if (factor == 0) { |
| 253 | Zero(); |
| 254 | return; |
| 255 | } |
| 256 | if (used_digits_ == 0) return; |
| 257 | |
| 258 | // The product of a bigit with the factor is of size kBigitSize + 32. |
| 259 | // Assert that this number + 1 (for the carry) fits into double chunk. |
| 260 | ASSERT(kDoubleChunkSize >= kBigitSize + 32 + 1); |
| 261 | DoubleChunk carry = 0; |
| 262 | for (int i = 0; i < used_digits_; ++i) { |
| 263 | DoubleChunk product = static_cast<DoubleChunk>(factor) * bigits_[i] + carry; |
| 264 | bigits_[i] = static_cast<Chunk>(product & kBigitMask); |
| 265 | carry = (product >> kBigitSize); |
| 266 | } |
| 267 | while (carry != 0) { |
| 268 | EnsureCapacity(used_digits_ + 1); |
| 269 | bigits_[used_digits_] = carry & kBigitMask; |
| 270 | used_digits_++; |
| 271 | carry >>= kBigitSize; |
| 272 | } |
| 273 | } |
| 274 | |
| 275 | |
| 276 | void Bignum::MultiplyByUInt64(uint64_t factor) { |
| 277 | if (factor == 1) return; |
| 278 | if (factor == 0) { |
| 279 | Zero(); |
| 280 | return; |
| 281 | } |
| 282 | ASSERT(kBigitSize < 32); |
| 283 | uint64_t carry = 0; |
| 284 | uint64_t low = factor & 0xFFFFFFFF; |
| 285 | uint64_t high = factor >> 32; |
| 286 | for (int i = 0; i < used_digits_; ++i) { |
| 287 | uint64_t product_low = low * bigits_[i]; |
| 288 | uint64_t product_high = high * bigits_[i]; |
| 289 | uint64_t tmp = (carry & kBigitMask) + product_low; |
| 290 | bigits_[i] = tmp & kBigitMask; |
| 291 | carry = (carry >> kBigitSize) + (tmp >> kBigitSize) + |
| 292 | (product_high << (32 - kBigitSize)); |
| 293 | } |
| 294 | while (carry != 0) { |
| 295 | EnsureCapacity(used_digits_ + 1); |
| 296 | bigits_[used_digits_] = carry & kBigitMask; |
| 297 | used_digits_++; |
| 298 | carry >>= kBigitSize; |
| 299 | } |
| 300 | } |
| 301 | |
| 302 | |
| 303 | void Bignum::MultiplyByPowerOfTen(int exponent) { |
| 304 | const uint64_t kFive27 = V8_2PART_UINT64_C(0x6765c793, fa10079d); |
| 305 | const uint16_t kFive1 = 5; |
| 306 | const uint16_t kFive2 = kFive1 * 5; |
| 307 | const uint16_t kFive3 = kFive2 * 5; |
| 308 | const uint16_t kFive4 = kFive3 * 5; |
| 309 | const uint16_t kFive5 = kFive4 * 5; |
| 310 | const uint16_t kFive6 = kFive5 * 5; |
| 311 | const uint32_t kFive7 = kFive6 * 5; |
| 312 | const uint32_t kFive8 = kFive7 * 5; |
| 313 | const uint32_t kFive9 = kFive8 * 5; |
| 314 | const uint32_t kFive10 = kFive9 * 5; |
| 315 | const uint32_t kFive11 = kFive10 * 5; |
| 316 | const uint32_t kFive12 = kFive11 * 5; |
| 317 | const uint32_t kFive13 = kFive12 * 5; |
| 318 | const uint32_t kFive1_to_12[] = |
| 319 | { kFive1, kFive2, kFive3, kFive4, kFive5, kFive6, |
| 320 | kFive7, kFive8, kFive9, kFive10, kFive11, kFive12 }; |
| 321 | |
| 322 | ASSERT(exponent >= 0); |
| 323 | if (exponent == 0) return; |
| 324 | if (used_digits_ == 0) return; |
| 325 | |
| 326 | // We shift by exponent at the end just before returning. |
| 327 | int remaining_exponent = exponent; |
| 328 | while (remaining_exponent >= 27) { |
| 329 | MultiplyByUInt64(kFive27); |
| 330 | remaining_exponent -= 27; |
| 331 | } |
| 332 | while (remaining_exponent >= 13) { |
| 333 | MultiplyByUInt32(kFive13); |
| 334 | remaining_exponent -= 13; |
| 335 | } |
| 336 | if (remaining_exponent > 0) { |
| 337 | MultiplyByUInt32(kFive1_to_12[remaining_exponent - 1]); |
| 338 | } |
| 339 | ShiftLeft(exponent); |
| 340 | } |
| 341 | |
| 342 | |
| 343 | void Bignum::Square() { |
| 344 | ASSERT(IsClamped()); |
| 345 | int product_length = 2 * used_digits_; |
| 346 | EnsureCapacity(product_length); |
| 347 | |
| 348 | // Comba multiplication: compute each column separately. |
| 349 | // Example: r = a2a1a0 * b2b1b0. |
| 350 | // r = 1 * a0b0 + |
| 351 | // 10 * (a1b0 + a0b1) + |
| 352 | // 100 * (a2b0 + a1b1 + a0b2) + |
| 353 | // 1000 * (a2b1 + a1b2) + |
| 354 | // 10000 * a2b2 |
| 355 | // |
| 356 | // In the worst case we have to accumulate nb-digits products of digit*digit. |
| 357 | // |
| 358 | // Assert that the additional number of bits in a DoubleChunk are enough to |
| 359 | // sum up used_digits of Bigit*Bigit. |
| 360 | if ((1 << (2 * (kChunkSize - kBigitSize))) <= used_digits_) { |
| 361 | UNIMPLEMENTED(); |
| 362 | } |
| 363 | DoubleChunk accumulator = 0; |
| 364 | // First shift the digits so we don't overwrite them. |
| 365 | int copy_offset = used_digits_; |
| 366 | for (int i = 0; i < used_digits_; ++i) { |
| 367 | bigits_[copy_offset + i] = bigits_[i]; |
| 368 | } |
| 369 | // We have two loops to avoid some 'if's in the loop. |
| 370 | for (int i = 0; i < used_digits_; ++i) { |
| 371 | // Process temporary digit i with power i. |
| 372 | // The sum of the two indices must be equal to i. |
| 373 | int bigit_index1 = i; |
| 374 | int bigit_index2 = 0; |
| 375 | // Sum all of the sub-products. |
| 376 | while (bigit_index1 >= 0) { |
| 377 | Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
| 378 | Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
| 379 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
| 380 | bigit_index1--; |
| 381 | bigit_index2++; |
| 382 | } |
| 383 | bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
| 384 | accumulator >>= kBigitSize; |
| 385 | } |
| 386 | for (int i = used_digits_; i < product_length; ++i) { |
| 387 | int bigit_index1 = used_digits_ - 1; |
| 388 | int bigit_index2 = i - bigit_index1; |
| 389 | // Invariant: sum of both indices is again equal to i. |
| 390 | // Inner loop runs 0 times on last iteration, emptying accumulator. |
| 391 | while (bigit_index2 < used_digits_) { |
| 392 | Chunk chunk1 = bigits_[copy_offset + bigit_index1]; |
| 393 | Chunk chunk2 = bigits_[copy_offset + bigit_index2]; |
| 394 | accumulator += static_cast<DoubleChunk>(chunk1) * chunk2; |
| 395 | bigit_index1--; |
| 396 | bigit_index2++; |
| 397 | } |
| 398 | // The overwritten bigits_[i] will never be read in further loop iterations, |
| 399 | // because bigit_index1 and bigit_index2 are always greater |
| 400 | // than i - used_digits_. |
| 401 | bigits_[i] = static_cast<Chunk>(accumulator) & kBigitMask; |
| 402 | accumulator >>= kBigitSize; |
| 403 | } |
| 404 | // Since the result was guaranteed to lie inside the number the |
| 405 | // accumulator must be 0 now. |
| 406 | ASSERT(accumulator == 0); |
| 407 | |
| 408 | // Don't forget to update the used_digits and the exponent. |
| 409 | used_digits_ = product_length; |
| 410 | exponent_ *= 2; |
| 411 | Clamp(); |
| 412 | } |
| 413 | |
| 414 | |
| 415 | void Bignum::AssignPowerUInt16(uint16_t base, int power_exponent) { |
| 416 | ASSERT(base != 0); |
| 417 | ASSERT(power_exponent >= 0); |
| 418 | if (power_exponent == 0) { |
| 419 | AssignUInt16(1); |
| 420 | return; |
| 421 | } |
| 422 | Zero(); |
| 423 | int shifts = 0; |
| 424 | // We expect base to be in range 2-32, and most often to be 10. |
| 425 | // It does not make much sense to implement different algorithms for counting |
| 426 | // the bits. |
| 427 | while ((base & 1) == 0) { |
| 428 | base >>= 1; |
| 429 | shifts++; |
| 430 | } |
| 431 | int bit_size = 0; |
| 432 | int tmp_base = base; |
| 433 | while (tmp_base != 0) { |
| 434 | tmp_base >>= 1; |
| 435 | bit_size++; |
| 436 | } |
| 437 | int final_size = bit_size * power_exponent; |
| 438 | // 1 extra bigit for the shifting, and one for rounded final_size. |
| 439 | EnsureCapacity(final_size / kBigitSize + 2); |
| 440 | |
| 441 | // Left to Right exponentiation. |
| 442 | int mask = 1; |
| 443 | while (power_exponent >= mask) mask <<= 1; |
| 444 | |
| 445 | // The mask is now pointing to the bit above the most significant 1-bit of |
| 446 | // power_exponent. |
| 447 | // Get rid of first 1-bit; |
| 448 | mask >>= 2; |
| 449 | uint64_t this_value = base; |
| 450 | |
| 451 | bool delayed_multipliciation = false; |
| 452 | const uint64_t max_32bits = 0xFFFFFFFF; |
| 453 | while (mask != 0 && this_value <= max_32bits) { |
| 454 | this_value = this_value * this_value; |
| 455 | // Verify that there is enough space in this_value to perform the |
| 456 | // multiplication. The first bit_size bits must be 0. |
| 457 | if ((power_exponent & mask) != 0) { |
| 458 | uint64_t base_bits_mask = |
| 459 | ~((static_cast<uint64_t>(1) << (64 - bit_size)) - 1); |
| 460 | bool high_bits_zero = (this_value & base_bits_mask) == 0; |
| 461 | if (high_bits_zero) { |
| 462 | this_value *= base; |
| 463 | } else { |
| 464 | delayed_multipliciation = true; |
| 465 | } |
| 466 | } |
| 467 | mask >>= 1; |
| 468 | } |
| 469 | AssignUInt64(this_value); |
| 470 | if (delayed_multipliciation) { |
| 471 | MultiplyByUInt32(base); |
| 472 | } |
| 473 | |
| 474 | // Now do the same thing as a bignum. |
| 475 | while (mask != 0) { |
| 476 | Square(); |
| 477 | if ((power_exponent & mask) != 0) { |
| 478 | MultiplyByUInt32(base); |
| 479 | } |
| 480 | mask >>= 1; |
| 481 | } |
| 482 | |
| 483 | // And finally add the saved shifts. |
| 484 | ShiftLeft(shifts * power_exponent); |
| 485 | } |
| 486 | |
| 487 | |
| 488 | // Precondition: this/other < 16bit. |
| 489 | uint16_t Bignum::DivideModuloIntBignum(const Bignum& other) { |
| 490 | ASSERT(IsClamped()); |
| 491 | ASSERT(other.IsClamped()); |
| 492 | ASSERT(other.used_digits_ > 0); |
| 493 | |
| 494 | // Easy case: if we have less digits than the divisor than the result is 0. |
| 495 | // Note: this handles the case where this == 0, too. |
| 496 | if (BigitLength() < other.BigitLength()) { |
| 497 | return 0; |
| 498 | } |
| 499 | |
| 500 | Align(other); |
| 501 | |
| 502 | uint16_t result = 0; |
| 503 | |
| 504 | // Start by removing multiples of 'other' until both numbers have the same |
| 505 | // number of digits. |
| 506 | while (BigitLength() > other.BigitLength()) { |
| 507 | // This naive approach is extremely inefficient if the this divided other |
| 508 | // might be big. This function is implemented for doubleToString where |
| 509 | // the result should be small (less than 10). |
| 510 | ASSERT(other.bigits_[other.used_digits_ - 1] >= ((1 << kBigitSize) / 16)); |
| 511 | // Remove the multiples of the first digit. |
| 512 | // Example this = 23 and other equals 9. -> Remove 2 multiples. |
| 513 | result += bigits_[used_digits_ - 1]; |
| 514 | SubtractTimes(other, bigits_[used_digits_ - 1]); |
| 515 | } |
| 516 | |
| 517 | ASSERT(BigitLength() == other.BigitLength()); |
| 518 | |
| 519 | // Both bignums are at the same length now. |
| 520 | // Since other has more than 0 digits we know that the access to |
| 521 | // bigits_[used_digits_ - 1] is safe. |
| 522 | Chunk this_bigit = bigits_[used_digits_ - 1]; |
| 523 | Chunk other_bigit = other.bigits_[other.used_digits_ - 1]; |
| 524 | |
| 525 | if (other.used_digits_ == 1) { |
| 526 | // Shortcut for easy (and common) case. |
| 527 | int quotient = this_bigit / other_bigit; |
| 528 | bigits_[used_digits_ - 1] = this_bigit - other_bigit * quotient; |
| 529 | result += quotient; |
| 530 | Clamp(); |
| 531 | return result; |
| 532 | } |
| 533 | |
| 534 | int division_estimate = this_bigit / (other_bigit + 1); |
| 535 | result += division_estimate; |
| 536 | SubtractTimes(other, division_estimate); |
| 537 | |
| 538 | if (other_bigit * (division_estimate + 1) > this_bigit) { |
| 539 | // No need to even try to subtract. Even if other's remaining digits were 0 |
| 540 | // another subtraction would be too much. |
| 541 | return result; |
| 542 | } |
| 543 | |
| 544 | while (LessEqual(other, *this)) { |
| 545 | SubtractBignum(other); |
| 546 | result++; |
| 547 | } |
| 548 | return result; |
| 549 | } |
| 550 | |
| 551 | |
| 552 | template<typename S> |
| 553 | static int SizeInHexChars(S number) { |
| 554 | ASSERT(number > 0); |
| 555 | int result = 0; |
| 556 | while (number != 0) { |
| 557 | number >>= 4; |
| 558 | result++; |
| 559 | } |
| 560 | return result; |
| 561 | } |
| 562 | |
| 563 | |
| 564 | static char HexCharOfValue(int value) { |
| 565 | ASSERT(0 <= value && value <= 16); |
| 566 | if (value < 10) return value + '0'; |
| 567 | return value - 10 + 'A'; |
| 568 | } |
| 569 | |
| 570 | |
| 571 | bool Bignum::ToHexString(char* buffer, int buffer_size) const { |
| 572 | ASSERT(IsClamped()); |
| 573 | // Each bigit must be printable as separate hex-character. |
| 574 | ASSERT(kBigitSize % 4 == 0); |
| 575 | const int kHexCharsPerBigit = kBigitSize / 4; |
| 576 | |
| 577 | if (used_digits_ == 0) { |
| 578 | if (buffer_size < 2) return false; |
| 579 | buffer[0] = '0'; |
| 580 | buffer[1] = '\0'; |
| 581 | return true; |
| 582 | } |
| 583 | // We add 1 for the terminating '\0' character. |
| 584 | int needed_chars = (BigitLength() - 1) * kHexCharsPerBigit + |
| 585 | SizeInHexChars(bigits_[used_digits_ - 1]) + 1; |
| 586 | if (needed_chars > buffer_size) return false; |
| 587 | int string_index = needed_chars - 1; |
| 588 | buffer[string_index--] = '\0'; |
| 589 | for (int i = 0; i < exponent_; ++i) { |
| 590 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
| 591 | buffer[string_index--] = '0'; |
| 592 | } |
| 593 | } |
| 594 | for (int i = 0; i < used_digits_ - 1; ++i) { |
| 595 | Chunk current_bigit = bigits_[i]; |
| 596 | for (int j = 0; j < kHexCharsPerBigit; ++j) { |
| 597 | buffer[string_index--] = HexCharOfValue(current_bigit & 0xF); |
| 598 | current_bigit >>= 4; |
| 599 | } |
| 600 | } |
| 601 | // And finally the last bigit. |
| 602 | Chunk most_significant_bigit = bigits_[used_digits_ - 1]; |
| 603 | while (most_significant_bigit != 0) { |
| 604 | buffer[string_index--] = HexCharOfValue(most_significant_bigit & 0xF); |
| 605 | most_significant_bigit >>= 4; |
| 606 | } |
| 607 | return true; |
| 608 | } |
| 609 | |
| 610 | |
| 611 | Bignum::Chunk Bignum::BigitAt(int index) const { |
| 612 | if (index >= BigitLength()) return 0; |
| 613 | if (index < exponent_) return 0; |
| 614 | return bigits_[index - exponent_]; |
| 615 | } |
| 616 | |
| 617 | |
| 618 | int Bignum::Compare(const Bignum& a, const Bignum& b) { |
| 619 | ASSERT(a.IsClamped()); |
| 620 | ASSERT(b.IsClamped()); |
| 621 | int bigit_length_a = a.BigitLength(); |
| 622 | int bigit_length_b = b.BigitLength(); |
| 623 | if (bigit_length_a < bigit_length_b) return -1; |
| 624 | if (bigit_length_a > bigit_length_b) return +1; |
| 625 | for (int i = bigit_length_a - 1; i >= Min(a.exponent_, b.exponent_); --i) { |
| 626 | Chunk bigit_a = a.BigitAt(i); |
| 627 | Chunk bigit_b = b.BigitAt(i); |
| 628 | if (bigit_a < bigit_b) return -1; |
| 629 | if (bigit_a > bigit_b) return +1; |
| 630 | // Otherwise they are equal up to this digit. Try the next digit. |
| 631 | } |
| 632 | return 0; |
| 633 | } |
| 634 | |
| 635 | |
| 636 | int Bignum::PlusCompare(const Bignum& a, const Bignum& b, const Bignum& c) { |
| 637 | ASSERT(a.IsClamped()); |
| 638 | ASSERT(b.IsClamped()); |
| 639 | ASSERT(c.IsClamped()); |
| 640 | if (a.BigitLength() < b.BigitLength()) { |
| 641 | return PlusCompare(b, a, c); |
| 642 | } |
| 643 | if (a.BigitLength() + 1 < c.BigitLength()) return -1; |
| 644 | if (a.BigitLength() > c.BigitLength()) return +1; |
| 645 | // The exponent encodes 0-bigits. So if there are more 0-digits in 'a' than |
| 646 | // 'b' has digits, then the bigit-length of 'a'+'b' must be equal to the one |
| 647 | // of 'a'. |
| 648 | if (a.exponent_ >= b.BigitLength() && a.BigitLength() < c.BigitLength()) { |
| 649 | return -1; |
| 650 | } |
| 651 | |
| 652 | Chunk borrow = 0; |
| 653 | // Starting at min_exponent all digits are == 0. So no need to compare them. |
| 654 | int min_exponent = Min(Min(a.exponent_, b.exponent_), c.exponent_); |
| 655 | for (int i = c.BigitLength() - 1; i >= min_exponent; --i) { |
| 656 | Chunk chunk_a = a.BigitAt(i); |
| 657 | Chunk chunk_b = b.BigitAt(i); |
| 658 | Chunk chunk_c = c.BigitAt(i); |
| 659 | Chunk sum = chunk_a + chunk_b; |
| 660 | if (sum > chunk_c + borrow) { |
| 661 | return +1; |
| 662 | } else { |
| 663 | borrow = chunk_c + borrow - sum; |
| 664 | if (borrow > 1) return -1; |
| 665 | borrow <<= kBigitSize; |
| 666 | } |
| 667 | } |
| 668 | if (borrow == 0) return 0; |
| 669 | return -1; |
| 670 | } |
| 671 | |
| 672 | |
| 673 | void Bignum::Clamp() { |
| 674 | while (used_digits_ > 0 && bigits_[used_digits_ - 1] == 0) { |
| 675 | used_digits_--; |
| 676 | } |
| 677 | if (used_digits_ == 0) { |
| 678 | // Zero. |
| 679 | exponent_ = 0; |
| 680 | } |
| 681 | } |
| 682 | |
| 683 | |
| 684 | bool Bignum::IsClamped() const { |
| 685 | return used_digits_ == 0 || bigits_[used_digits_ - 1] != 0; |
| 686 | } |
| 687 | |
| 688 | |
| 689 | void Bignum::Zero() { |
| 690 | for (int i = 0; i < used_digits_; ++i) { |
| 691 | bigits_[i] = 0; |
| 692 | } |
| 693 | used_digits_ = 0; |
| 694 | exponent_ = 0; |
| 695 | } |
| 696 | |
| 697 | |
| 698 | void Bignum::Align(const Bignum& other) { |
| 699 | if (exponent_ > other.exponent_) { |
| 700 | // If "X" represents a "hidden" digit (by the exponent) then we are in the |
| 701 | // following case (a == this, b == other): |
| 702 | // a: aaaaaaXXXX or a: aaaaaXXX |
| 703 | // b: bbbbbbX b: bbbbbbbbXX |
| 704 | // We replace some of the hidden digits (X) of a with 0 digits. |
| 705 | // a: aaaaaa000X or a: aaaaa0XX |
| 706 | int zero_digits = exponent_ - other.exponent_; |
| 707 | EnsureCapacity(used_digits_ + zero_digits); |
| 708 | for (int i = used_digits_ - 1; i >= 0; --i) { |
| 709 | bigits_[i + zero_digits] = bigits_[i]; |
| 710 | } |
| 711 | for (int i = 0; i < zero_digits; ++i) { |
| 712 | bigits_[i] = 0; |
| 713 | } |
| 714 | used_digits_ += zero_digits; |
| 715 | exponent_ -= zero_digits; |
| 716 | ASSERT(used_digits_ >= 0); |
| 717 | ASSERT(exponent_ >= 0); |
| 718 | } |
| 719 | } |
| 720 | |
| 721 | |
| 722 | void Bignum::BigitsShiftLeft(int shift_amount) { |
| 723 | ASSERT(shift_amount < kBigitSize); |
| 724 | ASSERT(shift_amount >= 0); |
| 725 | Chunk carry = 0; |
| 726 | for (int i = 0; i < used_digits_; ++i) { |
| 727 | Chunk new_carry = bigits_[i] >> (kBigitSize - shift_amount); |
| 728 | bigits_[i] = ((bigits_[i] << shift_amount) + carry) & kBigitMask; |
| 729 | carry = new_carry; |
| 730 | } |
| 731 | if (carry != 0) { |
| 732 | bigits_[used_digits_] = carry; |
| 733 | used_digits_++; |
| 734 | } |
| 735 | } |
| 736 | |
| 737 | |
| 738 | void Bignum::SubtractTimes(const Bignum& other, int factor) { |
| 739 | ASSERT(exponent_ <= other.exponent_); |
| 740 | if (factor < 3) { |
| 741 | for (int i = 0; i < factor; ++i) { |
| 742 | SubtractBignum(other); |
| 743 | } |
| 744 | return; |
| 745 | } |
| 746 | Chunk borrow = 0; |
| 747 | int exponent_diff = other.exponent_ - exponent_; |
| 748 | for (int i = 0; i < other.used_digits_; ++i) { |
| 749 | DoubleChunk product = static_cast<DoubleChunk>(factor) * other.bigits_[i]; |
| 750 | DoubleChunk remove = borrow + product; |
| 751 | Chunk difference = bigits_[i + exponent_diff] - (remove & kBigitMask); |
| 752 | bigits_[i + exponent_diff] = difference & kBigitMask; |
| 753 | borrow = static_cast<Chunk>((difference >> (kChunkSize - 1)) + |
| 754 | (remove >> kBigitSize)); |
| 755 | } |
| 756 | for (int i = other.used_digits_ + exponent_diff; i < used_digits_; ++i) { |
| 757 | if (borrow == 0) return; |
| 758 | Chunk difference = bigits_[i] - borrow; |
| 759 | bigits_[i] = difference & kBigitMask; |
| 760 | borrow = difference >> (kChunkSize - 1); |
| 761 | ++i; |
| 762 | } |
| 763 | Clamp(); |
| 764 | } |
| 765 | |
| 766 | |
| 767 | } } // namespace v8::internal |